Question

Выполните действия: _____________

Answer 1

$\displaystyle\tt\frac{a^2-1}{a^3+1}\cdot\frac{a^2-a+1}{a^2+2a+1}\cdot(a+1)=\\\\\\=\frac{(a-1)(a+1)}{(a+1)(a^2-a+1)}\cdot\frac{a^2-a+1} {(a+1)^2}\cdot(a+1)=\frac{a-1}{a+1}$

$\displaystyle\tt\frac{b^3-8}{b^2-9}\cdot\frac{b+3}{b^2+2b+4}=\frac{(b-2)(b^2+2b+4)}{(b-3)(b+3)}\cdot\frac{b+3}{b^2+2b+4}=\frac{b-2}{b-3}$

$\displaystyle\tt\frac{c^2+6c+9}{c^3+27}\cdot\frac{c^2-3c+9}{3c+9}=\frac{(c+3)^2}{(c+3)(c^2-3c+9)}\cdot\frac{c^2-3c+9}{3(c+3)}=\frac{1}{3}$